volume, shape, and shape position of rock fragments in openwork gravel

Volume, Shape, and Shape Position of Rock Fragments in Openwork GravelAuthor(s): Hakon WadellSource: Geografiska Annaler, Vol. 18 (1936), pp. 74-92Published by: Wiley on behalf of Swedish Society for Anthropology and GeographyStable URL: http://www.jstor.org/stable/519820 .

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VOLUME, SHAPE, AND SHAPE POSITION OF ROCK FRAGMENTS IN OPENWORK

GRAVEL. BY HAKON WADELL.

Scope of investigation.

T he investigation aims at a detail study of openwork gravel in a typical ose or esker and in the fore-set beds of a glacial delta. A part of the research has been

previously published (12), covering the sedimentographic analysis of shape and volume of the gravel fragments. The present paper deals mainly with shape positions of the rock fragments in the field, determined by the direction and angle of dip of the

longest axis of each fragment with reference to the magnetic meridian and the dip direction of the gravel bed.

Openwork or diakene gravel. The first description of openwork gravel is due to A. Erdman (3), in the year 1868.

He made the following observation in an ose (esker) north of the city of Falk6ping in Sweden. A free translation from the Swedish work reads: >One could observe a 40-50 feet long and 10-12 feet thick lense or stock-shaped deposit composed entirely of roll- stones with very little gravel between the fragments and surrounded on all sides by gra- velly or sandy layers.>

W. M. Davis (I) introduced in 1892 the term openwork gravel for such layers of gravel in which the space between the pebbles are empty, although the layers adjoining contain

plenty of fine material. J. Elbert (4) proposed in 1904 the term diakene (ode-xyvo-- between empty), a synonym of openwork.

Davis and Elbert described the openwork gravel as a common and characteristic feature of eskers. The former regarded it as an important link in the evidence leading to the explanation of the origin of eskers and interpreted it as indications of >hasty action, of whatever kind?. Referring to eskers ha said: #- - - it appears more probably that the delta growth was relatively rapid, the product of gushing streams laden with sand and gravel. This view is borne out by the structure of the openwork gravels above men- tioned in the eskers and in the coarser beds near the head of the plateau.?>

Elbert (4) gave the following description of openwork or diakene layers in oses (eskers): )Die diakenen Schichten sind meist regellos gebaut, doch bilden bisweilen die gr6ssten Gerlle den Kern. Bald handelt es sich nur um Linsen in einer Kiesbank, bald um selb-

standige Lagen. Wenn diakene mit normalen Kiesschichten wechsellagern, beobachtet man im Querschnitt meist eine schalige, im Lingsschnitt parallele Sonderung nach der

Gr6sse. Ferner werden die Ger6llagen oft durch nur wenige Millimeter starke Grand-, resp. Sandlagen getrennt, mit deren Vermehrung die Schirfe der Trennungsfuge zwischen Kies und Sand abnimmt.?



VOLUME, SHAPE, AND SHAPE POSITION OF ROCK FRAGMENTS 75

Miscellaneous terms and denotations.

The following gives the definitions of some previously introduced terms (9, 10, II, 12, 13, I4).

The diameter and the radius of a sphere of the same volume as a given, spherical or

non-spherical, solid are termed the true nominal diameter and the true nominal radius, denoted D. and r. respectively.

The sedimentologic shape expression is based on the isoperimetric property of a sphere and presented by the formula: s/S = y, where s is the surface area of a sphere of the same volume as the solid, s the actual surface area of the solid, and y denotes the degree of true sphericity. The maximum value obtained for y is I.ooo, which is the numerical shape value of a sphere.

It has been shown in previous papers (II, 12, 13) that the V-value has a close bearing upon the terminal, uniform settling velocity of a solid and upon the resulting coefficient of resistance as a function of Reynolds number. The practical difficulties, however, in

determining the surface area of an irregular rock fragment made it necessary to construct a formula suitable to rapid and practical methods. The following formulae were sug- gested:

' - d,,/Ds,

where TP'represents the value obtained by the ratio dl/Ds, d, denotes the true nominal diameter, and Ds represents the diameter of the smallest sphere cir-

cumscribing the rock-fragment, or practically the longest axis of the fragment. The maximum value obtained by this formula is I.ooo, which is the numerical shape value of a sphere. It was shown that this formula was suitable for solids for which the ratio

d,/Ds amounts to 0.8o or any higher value up to the maximum I.ooo. In the case that the ratio

d,,/Ds amounts to less than 0.8o the formula takes the following character:

q'= (d,/Ds) + 0.I.

Sixtytwo experimental determinations of the settling velocities of larger rock fragments of irregular shapes showed that the formulae given above were reasonably well in accord with the coefficient of resistance as function of Reynolds number of respective rockfragments in given sedimentation fluids (12).

The compass directions are in the following numbered clockwise, N.= 360~'0o, E.= 9o,

S.=I80', and W.=2700. (See figures 3 and 4.)

Sample localities.

The first investigation was made in an openwork gravel of the classical Adeline esker, the largest osetrain in northwestern Illinois, U. S. A. The locality is situated inside the southern part of the >McGrath pit>, at the southern foot of the esker, at Forreston, Ogle County, Illinois. The gravel is heavily coated with iron ocher with irregular streaks of

manganese ocher' (Mn3O,4-4H20). It occurs in more or less well defined layers, lenses and stocks with irregular bands of finer gravel and sand. The gravel bank, in which the

1 The term mangenese ocher has been adopted from De Geer and Fegraeus, who found similar deposits in the Swedish oses (2,5).



76 H A KON W A DELL

investigation was made, had a dip of approximately 320 towards I9o' clockwise (S. Ioo W.) from the magnetic North, thus more or less at right angles to the general trend of the southern side of the esker.

The second sample comes from the fore-set beds of a glacial delta deposit at Spring Valley, Bureau County, Illinois. The locality has for several years been exploited for

gravel and sand. The rockfragments occurred as openwork gravel in a more or less well- defined layer of I to 2 decimeters thickness with an average dip of 30' towards 2700

(West).

Field technic.

Instruments and tools: a Brunton Patent Pocket Transit; a soft pencil; two fine, point- ed and rather stiff brushes; two jars of rapid drying lacquer of red and black colour

respectively. The investigation was carried out on the vertical cuts of already existing excavations

left by operating sand and gravel companies. The gravel face was carefully examined, and fragments, which, by their loose and exposed situation, could be suspected to have

changed their original position, were removed. Gravel beds with an approximate dip of 30 degrees were sought on both localities, nota bene, in order to facilitate comparison and to eliminate such differences which eventually may occur in gravel beds of different dips.

The direction and angle of dip of the gravel bed were determined in customary manner. The direction of the gravel face, i. e. the trend of the vertical surface of the cut, was

carefully determined by repeated observations. The surface of the cut in the Adeline esker had the same trend as the dip of the gravel bed, i. e. towards 19o degrees clockwise from the magnetic North (N. Io0 E.-S. Io' W.). The cut in the Spring Valley deposit had a trend towards 265 degrees, thus differing but 5 degrees from the dip direction of to gravel bed (270 degrees).

Due to difficulties in describing the procedure of the field technic it has been necessary to illustrate the operations with somewhat distorted pictures. The rock fragment shown in Fig. I is disproportional large compared with the >Brunton> in the foreground. In reality few of the fragments were larger, and many were smaller than the compass.

Fig. I gives the operator's view of the >Brunton> when used as a prismatic compass. The image of the levels L, of the magnetic needle P and of the graduated compass circle is shown in the mirror M. The window 0 of the mirror permits observations of objects in the rear, and is used, in connection with the folding sight and the hair line bisecting the mirror, for locating a vertical line on the rock fragment. The line a,-a2 on the upper part of the lid is brought into a position parallel to the trend of the gravel face (previously determined) by observing in the mirror M the reflected image of the magnetic needle P. The horizontal position of the line a,--a2 is obtained by observing the image of the air bubbles of the levels L. The operator faces the vertical surface of the cut, and holding a soft pencil in the right hand and the compass in the left at the level of the eye, a line h--h12 parallel a--a2 is drawn with the pencil on about the middle of the exposed bulging sur-




face of the fragment. A vertical line v1-v2 is drawn at right angles to h---h2, holding the

compass in the same position as before. The vertical line coincides with the hair line of the mirror and with the center of folding sight and the window 0.

The pencil marks on the rock fragment are checked by repeating the observations,

holding the compass steady with both hands. The lines h1--h2 and v1-v2 are then coloured as narrow streaks of black and red lacquer respectively. The general dip direction (not the angle of dip) of the gravel bed is indicated on the fragment by a small black lacquer

P

M

o

Fig. i. The operator's view of the >Brunton,

in locating the guide lines on the rock fragment.

spot below and at the end of the black horisontal line (see Fig. I). The spot serves also as an indication of the position of the fragment, showing which part is the right and downward side.

The lacquer dries rapidly and has the advantage of not being obliterated even in rather

rough handling of the fragments in transportation. With a sufficient number of fragments painted, and the lacquer properly dried, the pebbles are detached from the gravel face and transported to the laboratory.

The area selected on the gravel face should be large enough to include approximately

Ioo to 2oo exposed rock fragments. A rectangular area parallel with the dip of the gravel bed is preferable. All fragments falling within the rectangular outline are marked and

painted, in order that no personal influence in selecting the fragments may occur. One hundred rock fragments from each of the two localities were deemed sufficient for the

present study.



78 H A K 0 N WA DELL

Laboratory technic.

The meridian and the equator appear as straight lines at right angles to each other, when a geographic globe is hold in a given position in front of the eye. If the globe is rotated on its vertical or on its horizontal axis, the meridian and the equator appear as bent lines respectively, the curvature of which increases as the globe rotates up to go degrees. The present study is based upon this principle. The black and red lines on the

bulging surface of a rock fragment correspond to the equator and the meridian respectively. The purpose is to reset the rock fragment in the laboratory in such position that

r 2

133

F 6

14-h

t18 4 Ng

Fig. 2. Apparatus used in the laboratory for determining the shape position of rock fragments.

the lines h1i-h2 and v1-v2 appear as straight lines in front of the eye. Knowing that these lines where drawn when the line a--a2 on the #Brunton) had a horizontal position parallel with the known trend of the gravel face, we have means of placing the rock fragment in the laboratory in the same position, which it had in the field with reference to the fixed trend of the vertical gravel face. The aim is to determine the trend and dip of the longest axis of each fragment with reference to direction and angle of dip of the gravel bed.

Fig. 2 illustrates an apparatus constructed on the simple means available in all mine-

ralogical laboratories. A rectangular window glass 1-2-3-4 is hold in vertical position by the rubber-shod pinchers 5, mounted on the stand z8. On the glass are drawn two

fine, black, lacquer lines 12-13 and Io--i at right angles to each other. A two-circle contact goniometer is placed behind the window glass in such position that the horizontal diameter of the vertical circle i6 is parallel with plane of the glass.' A piece of

1 In order to facilitate the description, Fig. 2 does not show the glass and the vertical circle in perfect parallel positions. In reality they should, however, be parallel. In order to show on a black and white drawing that the lines on the glass coincide and cover the lines on the rock fragment, it has been necessary to set the vertical circle slightly out of parallel position with the window glass.




putty, pitch or soft wax 14 is mounted on the crystal holder in the center of the horizontal circle 15. The shaded area F represents the rock fragment mounted on the putty 14. The ruler 6-7 is moved by means of the rod 17 along the graduated scale of the vertical circle I6.

Looking through the window glass the rock fragment F is, with help of both hands, mounted on the putty 14 in such position that the lines 12-13 and io--I of the glass coincide with and cover the lines v1-v2 and h1-h2 of the fragment respectively. (In respect to the anomaly in Fig. 2 see previous footnote.) The numerical values on the

graduated horizontal circle scale is then observed at a fixed point of the goniometer, and the number of degrees is recorded.

The trend of the longest axis 8-9 is found by viewing the fragment from different sides. The horizontal circle is then rotated till the longest axis of the fragment is parallel with the plane of the vertical circle i6, at which position the vertical circle by looking from above appears to coincide with and cover the longest axis of the fragment. The numerical value on the horizontal circle at a fixed point on the goniometer is again re-

corded, and the deviation from previous position is computed in degrees of rotation.

With the fragment remaining in the final position described above, the rod 17 is moved along the vertical circle i6 till the ruler 7-6 is parallel with the longest axis 8--9 of the fragment. The numerical value at the position of rod 17 on the vertical circle is

recorded, and the dip of the longest axis of the fragment is computed.1 Since the window glass represents the vertical gravel face, the trend of which was

determined in the field, the direction and angle of dip of the longest axis of the fragment is readily computed from values obtained in the laboratory. An example elucidates.

The vertical gravel face in the field trends towards 270 degrees clockwise from the

magnetic North. This trend is represented by the edge -z2 on the window glass. When the rock fragment has been placed in its proper position with its vertical and horizontal lines covered by corresponding lines on the window glass, the horizontal circle scale shows 5 degrees at a given fixed point. The horizontal circle together with the fragment is rotated, as the case may be, clockwise towards the operator till the longest axis of the

fragment, by observing from above, appears to coincide with the plane of the vertical circle. The horizontal circle scale is again read showing 25 degrees at the fixed point. Hence the fragment has rotated 20 degrees (25--5'=2o?) towards the operator. The trend of the dip of the longest axis is consequently 20 degrees in opposite direction. Since the window glass represents the gravel face of a trend towards 270 degrees, it follows that the dip direction of the longest axis of the fragment is towards 250 degrees (270'-

20o=2500) clockwise from the magnetic North. The determination of the angle of dip of the longest axis is simple, and an exemplification is therefore unnecessary.

1 On account of the difficulty in illustrating the operation it has been necessary to assume in the special case of Fig. 2 that the lines of the window glass coincide with those of the fragment when the longest axis of the pebble is parallel with the plane of the vertical circle. In all other cases the lines should not coincide after the rotation of the horizontal circle and the fragment.



80 HA KO N WADELL

Graphical representation of results.

Figures 3 and 4 are circle diagrams constructed to show the distribution of rock fragments with reference to direction and angle of dip of the longest axis of each fragment. The various directions are divided into class-intervals of io degrees each and numbered clockwise from the magnetic North. The angles of dip are arranged in classes of io degrees each from horizontal or o' to vertical or 90go. The hatched arrow across the diagram indicates the dip direction of the gravel bed.

In plotting the cases the value of the direction of the longest axis of the fragment determines the position clockwise. The dip angle value determines the position towards

t N. C"J 5 0 360 10 S4 O20

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Fig. 3. Circle diagram showing the, distribution of Ioo rock fragments classified according to direction and angle of dip of the longest axis of each fragment in the Adeline openwork gravel. Hatched arrow shows the

dip direction of the gravel bed.

Fig. 4. Circle diagram showing the distribution of ioo rock fragments classified according to direction and angle of dip of the longest' axis of each fragment in the Spring Valley openwork gravel. Hatched arrow shows the dip direction of the gravel bed.

the center of the diagram. A vertical axis is represented by a dot in the center of the field; a horizontal axis is shown by a dot on the outmost circle. Special care was exercised in determining the direction of a slight dip. In the choice between two opposite directions of a horizontal axis the case was always plotted on that side of the diagram which showed the greatest number of fragments of low dip angle.

Figures 3 and 4 show a remarkable contrast in distribution of the items with reference to the dip direction of the gravel beds (hatched arrows). The longest axes of the majority of fragments in the Adeline esker have more or less the same dip direction as the gravel bed, while the dip directions of the Spring Valley fragments generally trend in a direction




opposite to that of the gravel bed. These facts are graphically emphasized in the charts Figures 5 and 6.

Figures 5 and 6 present column diagrams, each showing the frequency distribution of 100 rock fragments classified according to orientation (direction) of dip of the longest axis of each fragment. The numerical values on the x-axis represent the orientation clockwise from the magnetic North in class-intervalls of 40 degrees each, or all together 9 classes (360/40 = 9). The frequency distribution is so arranged that the mode,1 or that point on the x-scale at which the concentration is greatest, i. e. the x-value corres-

ponding to the maximum ordinate, divides the x-axis in about two equal parts. The modal class, i. e. the class in which the mode falls, is located in the center of the x-axis, and

30

,20 E 00 E Lj-

o

10 Z1O

Mode f o ot w Orientation

0r erntat on

Fig. 5. Column diagram showing the frequency distribution of 1oo rock fragments classified according to orientation (direction) of dip of the longest axis of each fragment in the openwork gravel of the Adeline esker.

29

20

LA.

O e a 1 f So 2 . .. ...

Co q? ' , c Imv 0 Fig. 6. Column diagram showing the frequency distribution of 100 rock fragments classified according to orientation (direction) of dip of the longest axis of each fragment

in the Spring Valley openwork gravel.

with four of the eight remaining classes on each side. The dip direction of the gravel bed is indicated by a vertical fulldrawn line. Items falling exactly on a class-limit were

always given to the lower class.

Fig. 5 shows that the mode practically coincides with the dip direction of the bed, i. e. the longest axes of the majority of rock fragments have about the same dip direction as the gravel bed in the Adeline esker. The modal class has a striking high frequency,

1 The mode is computed according to the interpolation formula:

f12 Mode - I + X i

where 1 = lower limit of modal class. f, = frequency, of class next below modal class in value. f,= frequency of class next above modal class in value. i = class-interval.

F. C. Mills. Statistihal Methods, 1929, p. 128.

6. Geografiska Annaler 1936.



82 HAKON WADELL

14

c 20

0 iiii i

ti!i

0? 5"'10' 15- 20" 2,5" 30" 40' 50' 60- 70" 80. 9o* D i n

Fig. 7. Column diagram showing the frequency distribution of oo rock fragments classified according to angle of dip of the longest axis of each fragment in the Adeline

openwork gravel.

20

-A 1 0

4

I I "IoAr.ii-

E LA-i

tt

I ,

0* 5' 10* 15* 20* 25- 30* 40* 50 o 60" 70* so* o p

Fig. 8. Column diagram showing the frequency distribution of 100 rock fragments classified according to angle of dip of the longest axis of each fragment in the Spring

Valley openwork gravel.

and the distribution on each side is rather

regular, however, with a slight tendency of an increasing frequency in the direction

diametrically opposite the dip direction of the gravel bed.

Fig. 6, presenting the results obtained from the Spring Valley deposit, shows the mode and the dip of the gravel bed widely separated in diametrically opposite direc-

tions (compare also Fig. 4). The mode value amounts to 92.80 and the dip direction of the gravel bed is 2700. The distribution on each side of the modal class is much more

irregular than in Fig. 5. The hatched lines show the distribution, when those io fragments are eliminated which had a dip of one degree or less; hence almost horizontal

axes, the direction of which could not be considered accurately determined within the

margin of reliability of the method. Even with exclusion of the ten fragments the dia-

gram shows a rather high frequency in class

70o---100. The distribution of the fragments classi-

fied according to angle of dip of the longest axis is graphically presented in Figures 7 and 8. The numerical values on the x-axis

represent the angles of dip arranged in class- intervals of 5 degrees each.

The modal class in diagram Fig. 7 is located in class 150-2zoo, and the computed mode amounts to 16.40. The dip of the gravel bed is approximately 32 degrees or twice the

angle of dip of the longest axis of the ma-

jority of fragments (32/16 = 2). This fact means that the majority of fragments in the Adeline openwork gravel has reached a na-

tural stability on a 32 degrees slope, when the longest axis of each fragment has an

angle of dip approximately the half of the dip angle of the slope. Diagram Fig. 8 displays the results from the Spring Valley delta deposit. Fig. 8 B

shows that the axes of the majority of fragments have a very low angle of dip. Fig.8 A

presents the frequency distribution, when those io fragments are eliminated, the axes




of which had a dip of one degree or less. The computed mode (Fig. 8 A) amounts to 12.50 and, the dip of the gravel bed is approximately 30o; thus not far from twice the angle of dip of the majority of fragments, excluding pebbles of low dip angle. Hence the result is somewhat in analogy with that obtained from the Adeline esker. The modal class in Fig. 7 is, however, more pronounced than in Fig. 8 A, and the characteristic feature of the Spring Valley delta deposit is the great number of fragments of low dip angle.

Figures 9 and 10 present the frequency distribution of the rock fragments classified according to direction (orientation) and angle of dip of the longest axis of each fragment. The directions numbered clockwise from the magnetic North are divided into three fields A, B and C

(Fig. 9) of 120 degrees each, or 10'-130I3,

1300--2500, 2500--Io0 respectively (compare Fig. 3). One hundred fragments are distributed over the three sections A, B

and C. The numerical values on the x-axes represent the angles of dip arranged in class-intervals of 10 degrees each. The fragments falling within each field of orientation are classified according to the dip angle of the longest axis.

Fig. 9 shows that the modal classes of the three sections A, B and C fall in class

loo-2o0, and that the modal class of sec-

tion B has the highest frequency. These facts mean that the longest axes of the majority of rock fragments in the Adeline openwork gravel have approximately the same angle of dip regardless of the dip direction, and that there is a prevailing number of fragments (section B), the axes of which have approximately the same general dip direction as the gravel bed. (The dip direction 19oo of the gravel bed divides the orientation field 1300--2500 in two equal parts. Compare Fig. 3.)

Sections A1, B1 and C1 of Fig. 9 have been constructed with the purpose of eliminating visual differences between the sections A, B and C, due to disparity in the number of fragments falling within each field of orientation. Section B1 present the frequency in percentage instead of the actual number of frag-

!C ...

I I I I I....

II

IAI

0 -1I _

8 Orientation Orientation- 40 S10 -130 10-130

Ze tain- - Or nt 20-

E

, -

-

24

Orientation- Orientation-

8 Orientation o rientation 40 S130-250 130-250

80 0O 40

'p Di

0 a

0 i p - i p Fig. 9. Column diagram showing the frequency distribution of rock fragments classified according to orientation and angle of dip of the longest axis of each fragment in the Adeline openwork gravel.

to Orientation 270 -30

20 0. z.

50

Orientation o30 -30 - 150

40 Orientation 150-270

0 0, 10' 20' 30" 40" 50" 60 70 8 90

Dip

Fig. io. Column diagram showing the frequency distribution of rock fragments classified according to orientation and angle of dip of the longest axis of each fragment in the Spring Valley openwork

gravel.



84 HAKON WADELL

ments, i. e. the total number of fragments represented in section B has been taken as

Ioo per cent, and the percentage of fragments falling in each class is computed and plotted in section B1. The same calculations have been done in respect to sections A, A1 and C, C1. The diagram displays great similarity in respect to the modal classes of the sections A1, B1 and C1, a fact which goes to show that the longest axes of fragments within the three fields of orientation in the openwork gravel of the Adeline esker have a tendency towards an angle of dip of approximately i6 degrees or the half of the

angle of dip of the gravel bed (320).

Fig. Io presents the frequency distribution of the fragments from the Spring Valley delta deposit. The diagram is constructed in analogy with that of Fig. 9, A1,

BI and

C1, but the limits of the orientation fields are different, although the orientation classes have the same size, i. e. 1200 each. The frequency is given in percentage instead of the actual number of fragments. The hatched lines of the middle section 300-I500 show the outline of the diagram, when fragments of low dip angle (S I0) are eliminated. All sections of the diagram display a high frequency in class oo--Io as well as in class

o10-200, thus showing an unstable distribution on the lower dip angle classes, a fact which stands in notable contrast to the pronounced modal classes Io0--200 of diagram Fig. 9. The majority of fragments has a low dip angle, but there is also a rather high frequency present in the class io0-2o0. This fact seems to indicate that many fragments in the deposition process had had a tendency to assume a dip angle of approximately the half of the dip angle of the fore-set slope (300), thus in analogy with the Adeline openwork gravel, but that some contributive cause became decisive for the

positions of the majority of fragments of low dip angle.

The sedimentographic analysis. The details and the principles of the sedimentographic analysis have been described

in a previous paper (12). The following presents but an outline of the procedure. The volume of each rock fragment was determined by the common displacement

method in a graduated cylinder filled with water and of appropriate sixe according to the volume of the fragment. An accuracy within I cubic centimeter was aimed at for

larger pebbles. The volumes of smaller fragments were determined within a fraction of a cubic centimeter. The numerical value of the true nominal diameter, d,, was computed on the basis of the volumetric determination. The diameter of the smallest circum-

scribing sphere, Ds, or in this case the longest axis, was measured with a common ruler graduated in centimeters and millimeters. The T'-value was calculated according to formulae given previously in this article. The results are shown in the diagrams of

Figures II and 12. In the construction of the sedimentographic charts the frequency, or number of

fragments, was laid off along the y-axis, and the volume and l'-values on the x-axis. The size of the class-intervals are illustrated in the diagrams. Values falling exactly on a class-boundary were always given to the class of lower value.




An inspection of the diagrams shows that the openwork gravel of the Spring Valley delta deposit differs from that of the Adeline esker in the respect that the former displasy

X

-

------------------m - 0--------------------------4• mm •

2--

.40 .50 .60 .70 .80 .90 .00

Vo/ume (i cc

10JO 20 40 60 80 /00 50 ~O I 5 z'80

Fig. I I. Sedimentographic column diagrams showing the frequency distribution of Ioo rock fragments classified according to volume and q-value

of each fragment of the Adeline openwork gravel.

" , 3'30 0-- y

- -o--- . . .. -4- - S--8 " I--F ?i2-

.40 .50 .60 .70 .O .090 .00

0 70 20 0 60 JO /00 O50 200 250 S 80

Fig. 12. Sedimentographic columft diagrams showing the frequency distribution of Ioo rock fragments classified according to volume and q'-value

of each of the Spring Valley openwork gravel.

a comparatively great uniformity in regard to both volume and shape of the pebbles, while the latter shows a contrast between the statistical sorting in regard to volume size and shape. Attention is called to the fact that the two deposits show great simil-



86 HAKON WADELL

arity in respect to the shapes of the rock fragments. The diagrams have en almost identical appearance in regard to distribution of the fragments classified according to q'-value.

Summary and comparison.

Features of the openwork gravel of the Adeline esker: The longest axes of a prevailing number of fragments have more or less the same dip direction as the gravel bed. The axes of the majority of fragments have an angle of dip of approximately 16 degrees, or the half of the dip angle of the gravel bed. This holds regardless of the dip direction of the axes. The frequency distribution of the fragments classified according to volume size shows irregularity, and a wide size range.

Features of the openwork gravel of the Spring Valley fore-set bed: The axes of the majority of fragments have a dip direction more or less diametrically opposite to the dip direction of the gravel bed. The axes of a prevailing number of fragments have a low

dip angle, but a great number of pebbles has axes, the dip of which amounts to about 12.5 degrees, or approximately the half of the dip of the fore-set bed. The frequency distribution of the fragments classified according to volume size shows a pronounced central tendency and a rather short size range.

Common features of the two deposits: The beds of the two deposits have approximately the same dip, i. e. 320 and 300 respectively. The diagrams, illustrating the distribution of the fragments classified according to q'-value, display an almost identical appearance, showing great similarity in shape of the fragments of the two deposits. Although the central tendency and the size range of the fragments of the two localities show a notable disparity, the average size of the pebbles in the two deposits is not extraordinary different.

In conclusion, the common features related above may be eliminated in search of the cause to the differential features of the two deposits. In other words, the angle of dip of the gravel beds, and the size and shape of the rock fragments, being approximately the same in the two localities, do not explain the differences in respect to direction and

angle of dip of the fragments.

A tentative interpretation.

The glaciologist, who has camped at a steep slope of a frontal moraine of a glacier, has hardly escaped the experience of having his night's slumber disturbed by occasional roars of rolling stones or of the rustling sound of small avalanches of wet or semi-dry sand. The same may be observed in any large gravel pit with steep walls of sandy composition. Stone after stone becomes loosened from the sandy matrix and rolls down the slope, some landing on the lower part of the slope, others accumulating at the foot, while still others, usually the largest and most spherical ones, proceeding some distance from the foot before they come to rest. Occasionally the sand and the very finest gravel are set into motion downhill as a relatively thin layer, held together in part by the cohesion




between the particles, especially in wet or semi-dry condition. The sand layer sslides# down slowly, the motion being frequently arrested, but again started by additional material furnished from above. Gradually the sand layer #creeps# over the previously accumulated stones without filling the interstices.

Figures 13 and 14 give a broad view and a detail picture respectively of the >McGrath pit# of the Adeline esker. Fig. 13 shows coarse gravel deposited at an angle of rest and

'::: ':': :::"":': ::;::::-:'''i~:::: :':..........::: :

:cil-iili~iiii:-::-i.;?::-~i:- :-:ig'i;iii-iiiii~siiiii-ii:- ?:i~~i:-i-cii-:~i: -i~ii-ii~.. . .......... ::: :,m .......... ?34M?r?::: :::::~::

Fig. 13. View of the #McGrath pitb in the Adeline esker.

locally covered by sand and finer gravel, slid down from above. Fig. 14 gives a detail

picture of a slope having an angle of rest of approximately 30 degrees. The foreground displays rock fragments of great size range. Sand and finer gravel is visible further up to the left in background. The pictures illustrate openwork gravel in act of formation. It is only in spots where the coarser gravel becomes covered by sand and finer gravel, i. e. on such localities where a steep precipitate of sandy composition is present. The crossmark on Fig. 13 shows a spot of sand covering coarse gravel. The sand and finer

gravel have slid down from the, upper left (as indicated by the arrow) and covered the



88 H A K O N W A D E LL

larger rock fragments furnished from the higher precipitate in the rear. Fig. 15 shows the vertical cut in the ancient gravel openwork of the esker, or the locality where the measurements described in this paper were made.

Openwork gravel has been described as a rather common feature of oses and moraines. It usually occurs as layers and lenses of relatively small extent, varying in dip from a few degrees to almost vertical.) The latter case is found when the rock fragments have

...... ..

74?-

Fig. 14. Detail picture of a slope in the ))McGrath pit,•

of the Adeline esker.

been deposited between the steep side of frozen debris and a locally supporting ice wall.

Openwork gravel in eskers and moraines has often about the same angle of dip as the

angle of rest characteristic for slopes of subaerial deposits. The angle of repose of gravel and rock fragments in air varies from 30 to 40 degrees,

depending largely on the coarseness of the material and on the shape of the fragments. It does not usually exceeds 35 degrees. The talus slopes of Gaspe Peninsula reach an

angle of rest of up to 38-40 degrees according to Miner (6). The material comprising the slopes consists for the most part of angular, elongated calcareous slate fragments,




ranging in size from 0.5 inch to 5 inches in length, and I to 3 inches predominating. Miner gives the following description: >A close examination of the slopes disclosed the fact that each fragment, resting with its long axis parallel to the dip of the slope, was overlapped by the preceeding one forming an end and drag on each piece. The arrangement was so orderly that, viewed as a whole, it gave the appearance of having been laid by hand. The enechelon arrangement of the fragments and the elongated manner in which the rock weathers apparently accounts for the compactness and rigidity of the slopes.>

It has been shown that the axes of the majority of fragments in the Adeline openwork gravel have more or less the same dip direction as the gravel bed, thus in analogy with

.......

. . . . .

.!!ii

Fig. 15. The vertical cut in the ancient openwork gravel of the Adeline esker.

Miner's observations from the talus slopes of the Gaspe Peninsula. The fragments described by Miner have apparently pronounced elongated shapes, a fact which accounts for the conspicuous and readily observed conditions. The majority of fragments in the Adeline openwork gravel has a rather high degree of sphericity, and the longest axis of each fragment cannot be readily observed in the field, but requires more delicate determinations in the laboratory. It is reasonable to assume, however, that the conditions, observed in respect to pronounced elongated shapes, to some extent also shall be reflected in deposits composed of fragments of less conspicuous elongation.

The following facts observed in respect to the openwork gravel of the Adeline esker permit some tentative conclusions. The large size range of the fragments and the irregular distribution of the pebbles, classified according to volume size, indicate a source of rather unsorted material, such as may be found in a debris-filled glacier. The dip



90 H A K O N WA D E L L

directions of the longest axes of the fragments show some similarity to the conditions observed on the talus slopes of the Gaspe Peninsula, a fact suggesting that the Adeline

openwork gravel was deposited on a subaerial slope near the foot of the southern side of the esker, either at the margin of the ice, or more probably inside an ice tunnel between the ice wall and the side of the esker. Some fragments may have rolled down from the crest of the esker in act of forming; others were derived by dumping from the debris- filled roof and sides of the tunnel. Avalanches of outwashed material, composed of more or less unsorted sand and finer gravel, descended occasionally over the side of the esker in act of forming, covering the previously accumulated larger rock fragments without

filling the interstices. This explains the fact observed by Elbert (op. cit.) that sand of but few millimeters thickness frequent is found as intermittent layers in openwork gravel of oses and moraines. The openwork gravel (and in this case also the intermittent sand layers) is a gravitational deposit, i. e. an accumulation of rock fragments which

by the force of gravity alone, without any influence of the surrounding medium, have moved to the locality of deposition.1

The sedimentographic charts of openwork gravel from the Spring Valley delta de-

posit show that the gravel has been quite well sorted. The fact that the diagrams display a rather high degree of statistical sorting" in respect to both shape and volume size of the fragments indicates a good natural sorting.3

Schoklitsch (7) has given the following description of the processes involved in the formation of sand banks: )>Wandert eine Sandbank ahnlich einem Miindungsdelta in Stauwasser vor, so entsteht eine die ganze H6he der Sandbank umfassende Entmischung, derart, dass am Fusse der Sandbank das gr6bste Geschiebe liegt, wthrend sich in den oberen Schichten das feine ablagert. Vor jeder Sandbank wandert ndimlich ein Wirbel mit wagrechter Achse, durch den das fiber den Kopf gelangte grobe Geschiebe bis zum Fuss der Sandbank durchkollert, bzw. durchrutscht.)>

The processes, involved in tractional transportation over the top-set beds of a delta, sort out fragments of high degree of sphericity, because highly spherical fragments roll easier and with less interruptions than flat ones, i. e. fragments of low sphericity. This type of transportation involves also a sorting of the fragments according to their volume size (and specific gravity). There must be an upper limit for the size of highly

1 It should be noted that the imposing Adeline esker has every characteristic feature of an ose, and may be compared with the best Swedish specimens, yet the ridge cannot be interpreted as a marginal or subglacial delta for several reasons. There are no evidences of any contemporary sea or ice-dammed lake in the region.

The present paper is a part of yet unpublished material on the origin of eskers. A brief outline of a new hypothesis was published in 1932, (16).

2 Distinction is made between the statistical sorting and the natural sorting. The former reveals itself in the diagram. The natural sorting may express itself as a good statistical sorting, but the natural sorting may be good without corresponding statistical evidences. The degree of statistical sorting depends, among other factors, upon the sampling of the material. If the sample includes deposits by currents of greatly varying velocities, the diagram may present a picture of rather unsorted material, yet the natural sorting by each current velocity may have reach maximum per- fection under the given conditions. Although several attempts have been made by sedimentologists to give sorting a mathematical definition, none has as yet succeeded in obtaining a formula which stands criticism.

3 The reader is referred to pages 216-217 of paper 12.




spherical fragments which a current of a given average velocity is capable of setting into tractional motion, as well as a lower size limit of tractional fragments, determined

by particles of that size, shape, and specific gravity which the current is capable of

lifting into suspension. Rock fragments of such size and shape, that they fall between these two limits, are those which arrive by traction to the upper edge of the fore-set beds, where they roll or slide down the slope, the character of the motion depending on the surface and angle of the slope, and on the strength of the vortex of horizontal axis in front of the fore-set beds. The upward current produced by this vortex is opposed to the downward motion of the fragment, and may give rise to sliding of the pebble rather than rolling, provided that the slope is not too steep and the rock fragment not too large. The lift arising from the upward current will act in front of the center of mass of the fragment, and will tend to turn it upward about the rear of support. Since the static friction in the rear is relatively slight due to the lubricant properties of the water (8), the fragment slides down the slope by the force of gravitation. The

sliding will continue till the fragment lands on a more or less horizontal, or preferably somewhat backward, in proximal direction dipping #platform#, produced on the slope by the protruding part of a previously deposited rock fragment. (Many such #platforms# are visible on Fig. 14.) When the sliding fragment has come to rest on the >platform#, the longest axis of the pebble achieves a low dip angle, more or less conformable with the surface of the >platform#. - It is also likely that many fragments, perhaps the

majority having a proximal dip direction, achieve their position in sliding en masse, more or less according to the same mechanics which produce the wellknown proximal dip direction of pebbles in river beds. However, it is difficult to explain the openwork gravel on a 30 degrees slope of a fore-set bed as anything else but essentially a gravitational deposit formed by pebbles which have rolled and slid down from the top-set beds.

The present writer realizes that the investigation of but two deposits of openwork gravel are not enough to permit any definite conclusions. A presentation of new methods in determining the shape position of large sedimentary rock fragments is the main

purpose of this paper. The technic in the field as well as in the laboratory may be further

improved. The accuracy of the field measurements can be increased by the use of a tripod with ball and socket head attached to the #Brunton#. The laboratory technic may be

improved in effeciency by the use of an apparatus constructed for the purpose. A mecha- nism, by which the rock fragment can be rapidly and firmly attached on the center of the horizontal circle of the goniometer, is especially needed.

The author wishes to express his appreciation to Prof. J. H. Bretz of the University of Chicago, for guidance to the Adeline esker and the Spring Valley deposit; to the Chief of the State Geological Survey of Illinois, Dr. M. M. Leighton, for maps and informations about esker localities in the State of Illinois; and to Mr. E. Espenshade Jr. for assistance with measurements at the Spring Valley.



92 HAKON WADELL

References.

I. W. M. DAVIS, ,The

subglacial origin of certain eskers)>, Proceedings of the Boston Society of Na- tural History, Vol. 25, 1890-92, pp. 477-499.

2. G. DE GEER, >Om ett manganmineral i UppsalaAsen, )>Geol. Freningens i Stockholm F'rhandlingar, Bd. 6, 1882, pp. 42-44.

3. A. ERDMANN, )>Bidrag till kannedomen om Sveriges quartara bildningar,,

Sveriges Geologiska Undersdkning, Ser. C, No. I, 1868, p. 129.

4. J. ELBERT, )>Die Entwicklung des Bodenreliefs von Vorpommern und Riigen), VIII Jahres- bericht der Geographischen Gesellschaft zu Greifswald, I, 1904, p. 38.

5. T. FEGRAEUS. )Om f6rekomsten af manganockra i rullstens- och morangruse, Geol. Freningens i Stockholm F'rhandlingar, Bd. 8, 1886, pp. 170-171.

6. NEIL A. MINER, )>Talus Slopes of the Gasp6 Peninsula,> Science, Vol. 79, 1934, pp. 229-230.

7. A. SCHOKLITSCH, Geschiebebewegung in Fliissen und an Stauwerken, 1926, pp. 7-8. 8. O. TIETJENS und L. PRANDTL, Hydro- und Aeromechanik, Bd. I, 1931, p. 14. g. H. WADELL, )>Volume, Shape and Roudness of Rock Particles,)> Journ. Geol. Vol. 40, 1932, pp.

443-451. io. -, >Sphericity and Roundness of Rock Particles,), Jour. Geol. Vol. 41, 1933, PP. 3IO-331. 11. - , >The Coefficient of Resistance as a Function of Reynolds Number for Solids of Various

Shapes), Jour. Franklin Institute, Vol. 217, No. 4, 1934, PP. 459-490. 12. - , >Shape Determinations of Large Sedimental Rock-Fragments), Pan-American Geologist,

Vol. 61, 1934, pp. 187-220. 13. - , >Some New Sedimentation Formulas)), Physics, Vol. 5, No. 10, 1934, pp. 281-291. 14. - , )Volume, Shape and Roundness of Quartz Particles,), Jour. Geol. Vol. 43, 1935, pp. 250

-280. 16. -, >A Hypothesis on the Origin of Eskers), Bull. National Research Council, 89, Report of the

Committee on Sedimentation, 1930-32, pp. 223-225.



volume, shape, and shape position of rock fragments in openwork gravel

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